# Wheelbase

In both road and rail vehicles, the **wheelbase** is the distance between the centers of the front and rear wheels.

## Contents |

## Road

In automobiles, the **wheelbase** is the horizontal distance between the center of the front wheel and the center of the rear wheel. At equilibrium, the total torque of the forces acting on the car is zero, and thus the wheelbase is related to the force on each pair of tires by the following formula:

- <math>F_f = {d_r \over L}mg</math>

- <math>F_r = {d_f \over L}mg</math>

where <math>F_f</math> is the force on the front tires, <math>F_r</math> is the force on the rear tires, <math>L</math> is the wheelbase, <math>d_r</math> is the distance from the center of gravity (CG) to the rear wheels, <math>d_f</math> is the distance from the center of gravity to the front wheels (<math>d_f</math> + <math>d_r</math> = <math>L</math>), <math>m</math> is the mass of the car, and <math>g</math> is the gravity constant. So, for example, when one loads the truck with heavy goods, the center of gravity shifts rearward and the force on the rear tire increases causing it to sink to the extent that depends on the stiffness of the suspension. If the automobile is accelerating or decelerating, extra torque is placed on the rear or front tire respectively, and the equation relating the wheelbase, height above the ground of the CG, and the force on each pair of tires becomes:

- <math>F_f = {d_r \over L}mg - {h_{cg} \over L}ma</math>

- <math>F_r = {d_f \over L}mg + {h_{cg} \over L}ma</math>

where <math>F_f</math> is the force on the front tires, <math>F_r</math> is the force on the rear tires, <math>d_r</math> is the distance from the CG to the rear wheels, <math>d_f</math> is the distance from the CG to the front wheels, <math>L</math> is the wheelbase, <math>m</math> is the mass of the car, <math>g</math> is the acceleration of gravity (approx. 9.8 m/s^{2}), <math>h_{cg}</math> is the height of the CG above the ground, <math>a</math> is the acceleration (or deceleration if the value is negative). So, as is common experience, when the automobile accelerates, the rear usually sinks and the front rises depending on the suspension. Likewise, when braking the front noses down and the rear rises.:^{[1]}

Because of the effect the wheelbase has on the weight distribution of the vehicle, wheelbase dimensions are crucial to the balance and steering of the automobile. For example, a car with a much greater weight load on the rear tends to understeer due to the lack of the load (force) on the front tires and therefore the grip (friction) from them. This is why it is crucial, when towing a single-axle caravan, to distribute the caravan's weight so that down-thrust on the tow-hook is about 100 pounds force (400 N). Likewise, a car may oversteer or even "spin out" if there is too much force on the front tires and not enough on the rear tires. Also, when turning there is lateral torque placed upon the tires which imparts a turning force that depends upon the length of the tire distances from the CG. Thus, in a car with a short wheelbase, the short lever arm from the CG to the rear wheel will result in a greater lateral force on the rear tire which means greater acceleration and less time for the driver to adjust and prevent a spin out or worse.

Wheelbases provide the basis for one of the most common vehicle size class systems.

### Varying wheelbases within nameplate

Full-size cars such as the Jaguar XJ, Ford Crown Victoria, Lexus LS, BMW 7-Series, Audi A8 and Mercedes-Benz S-Class have had long wheelbase variants.

In contrast, coupe varieties of the Honda Accord, and Honda Civic usually have shorter wheelbases than the sedans that they were derived from.

### Bikes

The wheelbase on many commercially available bicycles and motorcycles is so short, relative to the height of their centers of mass, that they are able to perform stoppies and wheelies.

### Skateboards

In skateboarding the word 'wheelbase' is used for the distance between the two inner pairs of mounting holes on the deck. This is different than the distance between the rotational centers of the two wheel pairs. A reason for this alternative use is that decks are sold with prefabricated holes, but usually without trucks and wheels. It is therefore easier to use the prefabricated holes for measuring and describing this characteristic of the deck.

A common misconception is that the choice of wheelbase is influenced by the height of the skateboarder. However, the length of the deck would then be a better candidate, because the wheelbase affects characteristics useful in different speeds or terrains regardless of the height of the skateboarder. For example, a deck with a long wheelbase, say 16 inches (406.4 mm), will respond slowly to turns, which is often desirable in high speeds. A deck with a short wheelbase, say 14 inches (355.6 mm), will respond quickly to turns, which is often desirable when skating backyard pools or other terrains requiring quick or intense turns.

## Rail

In rail vehicles, the wheelbase follows a similar concept. However, since the wheels may be of different sizes (for example, on a steam locomotive), the measurement is taken between the points where the wheels contact the rail, and not between the centers of the wheels.

On vehicles where the wheelsets (axles) are mounted inside the vehicle frame (mostly in steam locomotives), the wheelbase is the distance between the front-most and rear-most wheelsets.

On vehicles where the wheelsets are mounted on bogies (amer.: trucks), three wheelbase measurements can be distinguished:

- the distance between the pivot points of the front-most and rear-most bogie;
- the distance between the front-most and rear-most wheelsets of the vehicle;
- the distance between the front-most and rear-most wheelsets of each bogie.

The wheelbase affects the rail vehicle's capability to negotiate curves. Short-wheelbased vehicles can negotiate sharper curves. On some larger wheelbase locomotives, inner wheels may lack flanges in order to pass curves.

The wheelbase also affects the load the vehicle poses to the track, track infrastructure and bridges. All other conditions being equal, a shorter wheelbase vehicle represents a more concentrated load to the track than a longer wheelbase vehicle. As railway lines are designed to take a pre-determined maximum load per unit of length (tonnes per meter, or pounds per foot), the rail vehicles' wheelbase is designed according to their intended gross weight. The higher the gross weight, the longer the wheelbase must be.

## See also

## References

- ↑ Ruina, Andy; Rudra Pratap (2002) (PDF).
*Introduction to Statics and Dynamics*. Oxford University Press. p. 350. http://ruina.tam.cornell.edu/Book/RuinaPratapNoProblems.pdf. Retrieved 2007-03-23.

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